A Discrete Probability Distribution and Some Applications

Some Functionals and Approximation Operators Associated with a Family of Discrete Probability Distributions

“…The probability distribution (a n,j,α,α ) j=0,1,••• ,n was investigated in [1]. In this paper, we extend the results from [1] to the distribution (a n,j,α,β ) j=0,1,••• ,n .…”

“…The probability distribution (a n,j,α,α ) j=0,1,••• ,n was investigated in [1]. In this paper, we extend the results from [1] to the distribution (a n,j,α,β ) j=0,1,••• ,n . This enlarges the family of the investigated distributions and the area of applications involving these distributions.…”

“…The probability distribution (a n,j,α ) j=0,1,••• ,n was investigated from several points of view in [1]. In this paper, we generalize the corresponding results by considering the distribution (a n,j,α,β [1]. A sequence of positive linear functionals is constructed in terms of the probability distribution.…”

“…The function h n,α,β (x) = H n,α+β,α (x) can be expressed also in terms of Appell polynomials. For further details, (see [1], Section 6).…”

“…Section 6 is devoted to inequalities between random variables from the preceding sections in the sense of the convex stochastic order. In the particular case α = 1 and β = 1/2 formula (33) was proved in [1].…”